For the flourless chocolate cake:

1. Preheat the oven to 350 degrees.
2. Fill a rectangular cake pan with very hot water about 2 inches up the sides of the pan and place on the bottom rack of the oven. This will make the oven a bit steamy and make the cake nice and moist.
3. Cut a 9″ round of parchment paper for the bottom of the pan.
4. Very generously grease the round cake pan with butter. I use a stick of butter. Once I’ve greased it I place 1 tablespoon of butter on a paper towel, place it in the microwave a few seconds until it is soft, and then grease the pan (bottom and sides) again, smearing the softened butter on every bit of the pan. This will ensure cake releases when removing it from the pan. Place the parchment paper on top of the greased pan and butter parchment paper as well.
5. Roughly chop the chocolate and cut the butter into pieces. Place chocolate and butter in the double broiler and stir until it has all melted and is velvety smooth.
6. Add the sugar, espresso powder, and vanilla extract to the chocolate mixture and whisk until combined.
7. Whisk in the cocoa powder, baking powder, and salt.
8. Pour the batter into the prepared pan and place the cake in middle of the oven rack, and bake for 30 minutes. The cake is done when you insert a cake tester into the center of the cake and it comes out clean.
9. Let the cake completely cool. Then run a sharp knife around the edges of the cake and invert it onto your serving plate. When ready to serve, pour some crème anglaise over each slice of cake and serve immediately.

For the crème anglaise:

1. Combine milk and cream in a heavy medium saucepan. Add vanilla and over medium-low heat, bring milk mixture to a simmer. Remove from heat.
2. Whisk egg yolks and sugar in a medium bowl to blend. Gradually whisk in the hot milk mixture into the yolk and sugar mixture. Return to saucepan and stir over low heat until custard thickens and coats the back of a spoon. It takes about 5 minutes (do not boil or overcook as the egg yolks will scramble). Strain sauce into a bowl. Cover and chill (can be made 1 day ahead).